The characterization of the vertical distribution of wind speed, V (h), is fundamental for an astronomical site for many different reasons: (i) the wind speed shear contributes to trigger optical turbulence in the whole troposphere; (ii) a few of the astroclimatic parameters, such as the wavefront coherence time (τ 0 ), depend directly on V (h); (iii) the equivalent velocity V 0 , controlling the frequency at which the adaptive optics systems have to run in order to work properly, depends on the vertical distribution of the wind speed and optical turbulence. Also, too strong a wind speed near the ground can introduce vibrations in the telescope structures. The wind speed at a precise pressure (200 hPa) has frequently been used to retrieve indications concerning τ 0 and the frequency limits imposed on all instrumentation based on adaptive optics systems. However, more recently, it has been proved that V 200 (the wind speed at 200 hPa) alone is not sufficient to provide exhaustive elements concerning this topic, and thus the vertical distribution of the wind speed is necessary. In this paper, we report on a complete characterization of the vertical distribution of wind speed strength, which has been carried out above Mt Graham (Arizona, USA), the site of the Large Binocular Telescope. We provide a climatological study extended over 10 yr using the operational analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF). We prove that this is representative of the vertical distribution of the wind speed at Mt Graham, with the exception of the boundary layer. We also prove that a mesoscale model can provide reliable nightly estimates of V (h) above this astronomical site from the ground up to the top of the atmosphere (∼20 km).